相关论文: Binary Matrix Completion Using Unobserved Entries

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most…

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…

This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…

We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…

Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires…

Complementary-label learning is a weakly supervised learning problem in which each training example is associated with one or multiple complementary labels indicating the classes to which it does not belong. Existing consistent approaches…

Matrix completion is a ubiquitous tool in machine learning and data analysis. Most work in this area has focused on the number of observations necessary to obtain an accurate low-rank approximation. In practice, however, the cost of…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…

With the rising penetration of distributed energy resources, distribution system control and enabling techniques such as state estimation have become essential to distribution system operation. However, traditional state estimation…

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

Recommender systems are seen as an effective tool to address information overload, but it is widely known that the presence of various biases makes direct training on large-scale observational data result in sub-optimal prediction…

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This…

A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and…

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…